1. Field of the Invention
This invention relates in general to radiation shield designs, and more particularly to an apparatus, method and program storage device for calculating high-energy neutron/ion transport to a target of interest.
2. Description of the Related Art
The capability to make diagnostic assessments of radiation exposure is needed to support a wide range of radiation exposure events. Moreover, the question of risk from radiation exposure is a much-debated topic of discussion. Every person receives daily “background” radiation from a variety of natural sources: from cosmic rays and radioactive materials in the Earth, from naturally occurring radionuclides in food, and from inhaling particulate decay products of radon gas. One area of increased radiation exposure risk to human results from advancing aircraft technology that allows higher operating altitudes thereby reducing the protective cover provided by the Earth's atmosphere from extraterrestrial radiations. This increase in operating altitudes is taken to a limit by human operations in space. Space radiation is likely to be the ultimate limiting factor for future human deep space exploration. Understanding the space radiation environment is essential for risk assessment of orbit/crew selection and provides the scientific basis of countermeasures for shielding materials (affecting flight weight/cost), radio-protectants, and pharmaceuticals. Every tissue/material/part installed on a space mission requires radiation risk analysis. While the present invention is described here with reference to spacecraft, those skilled in the art will recognize that the principles discussed herein and the embodiments of the invention described herein are also applicable to other applications and industries, such as aircraft design, material development, and proton cancer therapy.
The propagation of galactic ions through extended matter and determination of the origin of these ions has been the subject of many studies. For example, a one-dimensional equilibrium solution was proposed early to show that the light ions have their origin in the breakup of heavy particles. However, the one dimensional equilibrium solution did not include ionization energy loss and radioactive decay. Later, the one-dimensional propagation was shown to be simplistic and that leakage at the galactic boundary must be taken into account. The leakage was found to be approximated as a superposition of nonequilibrium one-dimensional solutions. A solution to the steady-state equations was given as a Volterra equation, which was solved to the first order in the fragmentation cross sections by ignoring energy loss. This provided an approximation of the first-order solution that included ionization energy loss and was only valid at relativistic energies. An overview of the cosmic ray propagation was later provided. A derivation of the Volterra equation included the ionization energy loss, but evaluated only the unperturbed term.
These studies focused on only achieving first-order solutions in the fragmentation cross sections where path lengths in the interstellar space are approximately 3 to 4 g/cm2. However, higher order terms cannot be ignored in accelerator or space shielding transport problems. In addition to this simplification, previous cosmic ray models have neglected the complicated three-dimensional nature of the fragmentation process.
Several approaches to the solution of high-energy heavy ion propagation that include ionization energy loss have been developed during the last 20 years. However, most have assumed the straight-ahead approximation and velocity-conserving fragmentation interactions, whereas only a few have incorporated energy-dependent cross sections. An approach examining a primary ion beam represented the first-generation secondary fragments as a quadrature over the collision density of the primary beam. An energy multigroup method was used in which an energy-independent fragmentation transport approximation was applied within each energy group after which the energy group boundaries were moved according to continuous slowing-down theory. The energy-independent fragment transport equation was solved with primary collision density as a source and neglected higher order fragmentation. The primary source term extended only to the primary ion range from the boundary and the energy-independent transport solution was modified to account for the finite range of the secondary fragment ions.
An expression was derived for the ion transport problem to the first-order (i.e., first-collision) term and gave an analytical solution for the depth-dose relationship. The more common approximations used in solving the heavy ion transport problem were further examined. The effect of conservation of velocity on fragmentation and on the straight-ahead approximation was found to be negligible for cosmic ray applications. Solution methods for representation of the energy-dependent nuclear cross sections were derived. The energy loss term and the ion spectra were approximated by simple forms for which energy derivatives were evaluated explicitly. The resulting ordinary differential equations in terms of position were solved analytically. This approximation results in the decoupling of motion in space and a change in energy. The energy shifts were replaced by an effective attenuation factor. Later, the next higher order (i.e., second-collision) term was added. The second-collision term was found to be very important in describing 20 Ne beams at 670 A MeV. The three-term expansion was modified to include the effect of energy variation of the nuclear cross sections. The integral form of the transport equation was also used to derive a numerical marching procedure to solve the cosmic ray transport problem. This method accommodated the energy-dependent nuclear cross sections within the numerical procedure. Comparison of the numerical procedure with an analytical solution of a simplified problem validated the solution technique to approximately 1-percent accuracy. Several solution techniques and analytical methods have also been developed for testing future numerical solutions of the transport equation. More recently, an analytical solution for the laboratory ion beam transport problem has been derived with a straight-ahead approximation, velocity conservation at the interaction site, and energy-dependent nuclear cross sections.
From an overview of these past developments, the applications are divided into two categories: a single-ion species with a single energy at the boundary and a broad host of elemental types with a broad continuous energy spectrum. Techniques, which will represent the spectrum over an array of energy values, require vast computer storage and computation speed to maintain sufficient energy resolution for the laboratory beam problem. In contrast, analytical methods, which are applied as a marching procedure have similar energy resolution problems. This is a serious limitation because a final (i.e., production) high-charge-and-energy (HZE) computation method for cosmic ray shielding must be thoroughly validated by laboratory experiments. Some researchers hope for a single code, which can be validated in the laboratory and used in space applications. More recently, a Green's function has been derived which can be tested in the laboratory and used in space radiation protection applications.
Lastly, the problems of free-space radiation transport and shielding has been addressed using a high-charge-and-energy (HZE) transport computer program, which is referred to as the HZETRN program. The HZETRN program (referred to herein as 1995 HZETRN) has been widely used in prior shield design verification and validation processes. Additionally, the BRYNTRN code, discussed in F. A. Cucinotta, “Extension of the BRYNTRN code to monoenergetic light ion beams,” NASA TP-3472, 1994, is a baryon transport code used to calculate the energy spectrum of secondary nucleons, and has been widely used. 1995 HZETRN is described in detail by J. W. Wilson et al. in “HZETRN: Description of a Free-Space Ion and Nucleon Transport and Shielding Computer Program,” NASA TP-3495, May 1995, which is hereby incorporated by reference in its entirety. 1995 HZETRN is designed to provide fast and accurate dosimetric information for the design and construction of space modules and devices. The program is based on a one-dimensional space-marching formulation of the Boltzmann transport equation with a straight-ahead approximation. The general Boltzmann equation was simplified by using standard assumptions to derive the straight-ahead equation in the continuous slowing-down approximation and by assuming that heavy projectile breakup conserves velocity. The effect of the long-range Coulomb force and electron interaction was treated as a continuous slowing-down process. Atomic (electronic) stopping power coefficients with energies above a few A MeV were calculated by using Bethe's theory including Bragg's rule, Ziegler's shell corrections, and effective charge. Nuclear absorption cross sections were obtained from fits to quantum calculations and total cross sections were obtained with a Ramsauer formalism. Nuclear fragmentation cross sections were calculated with a semi-empirical abrasion-ablation fragmentation model. An environmental model was also used to provide input to the HZE transport computations.
Nevertheless, improved spacecraft shield design to support planned missions to the moon and Mars requires early entry of radiation constraints into the design process to maximize performance and minimize costs. Of particular importance is the need to implement probabilistic models to account for design uncertainties in the context of optimal design processes. These requirements need supporting tools with high computational efficiency to enable appropriate design methods.
Accordingly, there is a need for an apparatus, method and program storage device for calculating high-energy neutron/ion transport to a target of interest.
It can also be seen that there is a need for an improved radiation shield design apparatus, method and program storage device that implements improvements to the database, basic numerical procedures, and algorithms along with new methods of verification and validation to capture a well defined algorithm for engineering design processes to be used in an early development phase of space exploration shield designs.